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On the probability generating function of the sum of Markov Bernoulli random variables

Published online by Cambridge University Press:  14 July 2016

J. Gani
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Abstract

A direct proof of the expression for the limit probability generating function (p.g.f.) of the sum of Markov Bernoulli random variables is outlined. This depends on the larger eigenvalue of the transition probability matrix of their Markov chain.

Keywords

MARKOV BERNOULLI RANDOM VARIABLESTRANSITION PROBABILITY MATRIXEIGENVALUESLIMIT P.G.F.
Type
Part 6 — Stochastic Processes
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 321 - 326
Copyright
Copyright © 1982 Applied Probability Trust 

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References

Bartlett, M. S. (1978) An Introduction to Stochastic Processes , 3rd edn. Cambridge University Press.Google Scholar
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Edwards, A. W. F. (1960) The meaning of binomial distribution. Nature, London 186, 1074.Google Scholar
Wang, Y. H. (1981) On the limit of the Markov binomial distribution. J. Appl. Prob. 18, 937–942.Google Scholar